Quadratic Vote Buying

Abstract

A group of individuals with access to transfers seeks to make a binary collective decision. All known mechanisms they might use are either are often inefficient (e.g. voting), subject to severe collusion problems (e.g. the Vickrey-Clarke-Groves mechanism) or require the planner being informed about the distribution of valuations (e.g. the Expected Externality mechanism). I propose a simple, budget-balanced mechanism inspired by the work of Hylland and Zeckhauser (1979). Individuals purchase votes with the cost of a marginal vote being linear in the number of votes purchased; thus the total cost of votes is quadratic in the number purchased. The revenues earned from that individual are then refunded to other individuals. When there are a large number of individuals, this Quadratic Vote Buying mechanism is efficient in any Bayesian equilibrium under symmetric independent private values and is usually nearly efficient even with aggregate uncertainty. Collusion by a small group or individuals' taking on (a small number of) multiple identities does not significantly reduce efficiency.